*2.3. Boundary Conditions*

Figure 1 describes the boundary conditions of the simulation. For the tube, the pressure-outlet boundary condition was applied at the two tube exits with a constant value of 101.325 Pa (1/1000 atm). The pod and the tube walls are stationary walls with no-slip and adiabatic conditions. The pod was placed at a fixed position and instantly starts to move from right to left at a specified speed. Eight pod speeds were considered, from 100 to 350 m/s. Meanwhile, the pod-mesh zone also moved with the same speed and in the same direction as the pod.

The Reynolds number (*Re*) was calculated using the formula *Re* = ρ*vPdh*/μ, where ρ, *vP*, *dh*, and μ are the reference air density, pod speed, hydraulic diameter, and viscosity, respectively. The hydraulic diameter *dh* = *dtube* − *dpod* was determined as 2 m for BR = 0.36 and 3 m for BR = 0.25. Hence, for the range of pod speed considered in this study, the Reynolds number *Re* ranged from 13 × 10<sup>3</sup> to 45 × 10<sup>3</sup> for BR = 0.36, which indicates turbulent flow. Table 2 shows the variation of the Reynolds number *Re* with respect to the increase in pod speed. As the pod speed increases, the Reynolds number *Re* also increases. As BR increases, the Reynolds number *Re* decreases.

**Table 2.** Variation of Reynolds number (*Re*) with respect to pod speed and BR.


The simulations in this study were carried out under unsteady conditions. The variation of drag and the propagation of compression waves in Figure 4 show that the drag and compression waves tend to stabilize after 0.2 s. Owing to this stationary condition, one second of simulation time was enough to fully develop the flow field and investigate the behavior of the pressure waves. Therefore, in this study, we took a total simulation time of 1 s. The values of drag were estimated at 1 s, and results of pressure waves were exported after initial transients. In the steady-state condition, the pressure wave propagation cannot be examined. Furthermore, the pressure waves that arrive at the boundaries may alter the specified boundary conditions and a ffect drag evaluation. Hence, the unsteady-state simulation was used to explain the pressure wave phenomenon, as well as estimate the drag variation more accurately.

(**b**) Compression wave propagation (<sup>ݒ</sup> = 350 m/s)

**Figure 4.** Variation of (**a**) drag and (**b**) compression wave propagation with respect to time in unsteady conditions. All results after the initial transients are analyzed.
